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A133161
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Indices of the triangular numbers which are also centered triangular number.
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2
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1, 4, 16, 61, 229, 856, 3196, 11929, 44521, 166156, 620104, 2314261, 8636941, 32233504, 120297076, 448954801, 1675522129, 6253133716, 23337012736, 87094917229, 325042656181, 1213075707496, 4527260173804, 16895964987721
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OFFSET
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1,2
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COMMENTS
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Also, indices of the triangular numbers which are sums of three consecutive triangular numbers (see A129803).
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LINKS
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FORMULA
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a(n+2)=4*a(n+1)-a(n)+1.
a(n+1)=2*a(n)+0.5+0.5*(12*a(n)^2+12*a(n)-15)^0.5.
G.f.: x*(1-x+x^2)/(1-x)/(1-4*x+x^2). - R. J. Mathar, Oct 24 2007
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MATHEMATICA
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LinearRecurrence[{5, -5, 1}, {1, 4, 16}, 30] (* Harvey P. Dale, Aug 29 2017 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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